I am currently trying to get the posts for a specific user from Facebook's Graph API. I have done this numerous times before using a php script I have developed; but the problem this time seems to be on Facebook's end, not mine.

I am trying to get the posts from (replacing TOKEN with an access token):

The graph won't show any posts by the owner of that page but will show everyone else's posts, and as far as I can see the posts are marked as public, and there are no privacy settings set on the account that would stop it from adding the posts to the graph.

You need to check the "profile" privacy settings (what to share with apps). But most importantly, this is against Facebook ToS!
You can't use a user profile to represent your business, you need to use Facebook pages instead!

Why should I convert my profile (timeline) to a Page?
Since profiles
(timelines) are for meant individual people, they aren't suited to
meet your business needs. Pages offer more robust features for
organizations, businesses, brands, and public figures, which you can
learn more about here.

Further, maintaining a profile (timeline) for anything other than an
individual person is a violation of Facebook's Statement of Rights and
Responsibilities. If you don’t convert your profile (timeline) to a
Page, you risk permanently losing access to the profile (timeline) and
all of your content.